Kabul, Afghanistan (CNN) -- Militants staged attacks on government buildings in the restive southern Afghan city of Kandahar on Saturday, a brazen Taliban onslaught designed to seize or kill the provincial governor.

A National Directorate of Security official, who asked not to be named for security reasons, told CNN that an unknown number of people were killed and 30 others, including civilians, were wounded.

The Taliban -- which claimed responsibility for the strikes -- said the assault is part of its Bader operation, the codename for the group's spring offensive launched last week.

"This operation is a part of the Bader seasonal operation and the aim of this was to arrest or kill the governor of the Kandahar, and demoralize the Afghan and international forces in Afghanistan," Taliban spokesman Qari Yousof Ahmadi told CNN.

NATO's International Security Assistance Force said the attacks began with a combined rocket-propelled grenade attack and small arms fire on the province governor's compound and followed with assaults on an array of targets.

Taliban and a provincial governor's spokesman said targets included the National Directorate of Security, a police headquarters, the Kandahar city headquarters, and the provincial governor's office.

ISAF said the Afghanistan National Chief of Police Headquarters, the Transportation Police Headquarters, Police Sub-station One and various ANSF and ISAF buildings in Kandahar City and the Arghandab River Valley were attacked.

Police officers were among the wounded, said Zelmai Ayoubi, a spokesman for the Kandahar governor.

Maryam Dorani, a member of Kandahar's provincial council, said the Taliban fighters were using a high school as a shooting position on the governor's office.

ISAF said there were reports of more than five suicide bombers utilizing vehicle-borne explosive devices were involved in the attack.

Ayoubi said that from the beginning of this attack, "more then 10 explosions have been happened across Kandahar city."

Afghan security forces prevented three car bombs from detonating and provided perimeter security with ISAF, and ISAF said there was no word of insurgent attacks breaching the perimeters of any of the compounds, the alliance said.

"Initial reports indicate that between three and six suicide bombers were stopped -- either detonating prematurely or being killed before they could detonate," ISAF said.

U.S. Marine Corps Maj. Gen. James B. Laster, an ISAF spokesman, said Afghan forces thwarted a "spring offensive spectacular attack" that wounded civilians, who the Taliban vowed to protect.

"Afghan National Security Forces responded calmly and capably and with limited ISAF assistance, were able to restore calm to the city," he said.

President Hamid Karzai claimed the assault was an act of revenge over U.S. forces killing Osama bin Laden's death. He condemned Saturday's attacks. He also deplored the militants' use of schools to launch strikes, an action that he said underscores their embrace of terrorism and disdain for education. He made the remarks during a trip to Turkey.

Afghan officials said gunfights between security forces and militants persisted later Saturday in various locations across Kandahar city. Both Kandahar city and the province of the same name have been major fronts in the Afghan war.

The Taliban assault came a day after the group confirmed the killing of al Qaeda leader Osama bin Laden, slain in a U.S. military raid in Pakistan on Monday.

The militant group, which harbored bin Laden's terror network when it attacked the United States on September 11, 2001, said bin Laden's death will give "new impetus to current Jihad."

"Today's operation was planned a week ago and we will think about the attacks about revenges of the Sheikh Osama's murder in the future," Ahmadi said.

Bader, the name of the Taliban's offensive, is a reference to a battle in the early days of Islam, when the Prophet Mohammed is believed to have successfully led a key fight against non-Muslims.